Geophysical flows under location uncertainty, Part I Random transport and general models

TL;DR

This paper introduces a stochastic flow model for geophysical flows that decomposes velocity into large-scale and turbulent components, leading to a novel energy-conserving stochastic transport framework with broad applications.

Contribution

It develops a new stochastic transport operator incorporating drift correction, anisotropic diffusion, and multiplicative noise, with proven energy conservation, advancing geophysical flow modeling.

Findings

Energy conservation holds for all realizations of the stochastic flow.

The stochastic operator enables new formulations of classical geophysical flow models.

The approach effectively captures effects of small-scale turbulence in large-scale flows.

Abstract

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction , an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.